Gallagher is being linked with Aston Villa and Tottenham.
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But he said from the England camp: “I’m a Chelsea player right now and like I said I am just focused on England and the tournament.
“I have just been focusing on England, this is the most important thing right now for me, for the country and I just want to start the tournament now.
“It is not difficult, I’m in a very privileged position to play for England and be at a tournament like this and I couldn’t be happier with the situation.”